Being a numerically exact method for the simulation of dynamics in open quantum systems, the hierarchical equations of motion (HEOM) approach still suffers from the curse of dimensionality. In this study, we propose a novel multiconfigurational Ehrenfest (MCE)-HEOM method, which introduces the MCE ansatz to the second quantization formalism of HEOM. Here, the MCE equations of motion are derived from the time-dependent variational principle in a composed Hilbert–Liouville space, and each MCE coherent-state basis can be regarded as having an infinite hierarchical tier such that the truncation tier of auxiliary density operators in MCE-HEOM can also be considered to be infinite. As demonstrated in a series of representative spin-boson models, our MCE-HEOM significantly reduces the number of variational parameters and could efficiently handle the strong non-Markovian effect, which is difficult for conventional HEOM due to the requirement of a very deep truncation tier. MCE-HEOM is further applied to the 7-site Fenna–Matthews–Olson complex to study energy transfer in photosynthesis, and the results indicate that multi-site and multi-bath cases can also be accurately described with high efficiency. Compared to MCE, MCE-HEOM reduces the number of effective bath modes and circumvents the initial sampling for finite temperatures, eventually resulting in a significant reduction in computational cost.
Shi et al. (Mon,) studied this question.